Simplify the following expression: $ z = \dfrac{3}{10} - \dfrac{k + 7}{k - 4} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 4}{k - 4}$ $ \dfrac{3}{10} \times \dfrac{k - 4}{k - 4} = \dfrac{3k - 12}{10k - 40} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{k + 7}{k - 4} \times \dfrac{10}{10} = \dfrac{10k + 70}{10k - 40} $ Therefore $ z = \dfrac{3k - 12}{10k - 40} - \dfrac{10k + 70}{10k - 40} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{3k - 12 - (10k + 70) }{10k - 40} $ Distribute the negative sign: $z = \dfrac{3k - 12 - 10k - 70}{10k - 40}$ $z = \dfrac{-7k - 82}{10k - 40}$